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sammy [17]
1 year ago
13

Which of the following inequalities has no solutions?

Mathematics
1 answer:
neonofarm [45]1 year ago
8 0

Answer:

  • A) x > 3 and x < 2 has no solutions

Step-by-step explanation:

Given inequalities below and we are looking for a pair with no solution.

Let's verify:

A) x > 3 and x < 2,

  • It has no solutions since the two inequalities have no common interval.

B) x > - 3 and x < - 2,

  • Its solution is -3 < x < - 2, the interval between two given endpoints.

C) x > - 3 and x < 2,

  • Similar to option B, the interval is between two endpoints:
  • - 3 < x < 2

D) x > - 3 and x > - 2,

  • Its solution is x > - 2, the two inequalities cover almost same interval.
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Angle of the Sun A 96-ft tree casts a shadow that is 120 ft long. What is the angle of elevation of the sun
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Answer:

The angle of elevation of the sun is 39⁰

Step-by-step explanation:

Given;

height of the tree, h = 96 ft

length of the shadow, L = 120 ft

                                                   |

                                                   | 96ft

                                                   |

                                                   |

       θ------------------------------------

                    120ft

Completing this triangle to cut across the top of the tree gives you a right angled triangle with θ as the angle of elevation of the sun.

Apply trig-ratio to determine the angle of elevation of the sun;

tanθ = opposite side / adjacent side

tanθ = 96 / 120

tanθ = 0.8

θ = tan⁻¹(0.8)

θ = 38.7⁰

θ = 39⁰

Therefore, the angle of elevation of the sun is 39⁰

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